Writing Equations Presented By Mr. G. Laws 8thMath/Algebra 1

Standard(s) Math 1 – A.CED.1- Create equations and inequalities with one variable and use them to solve problems. 8 th Grade Mathematics – 8.EE.7- Solve linear equations in one variable.

Essential Question O Using math principles, how can you solve real world problems by writing and solving a linear equation?

Writing Equations O Writing equations is one strategy you can use to solve linear equations or real world problems. O You must be able to identify the variable that represents an unidentified number or measure referred within the problem. O Then you write a verbal expression as an algebraic expression or equation.

Key Words AdditionSubtractionMultiplicationDivisionEqual (=) Plus Increase Sum Add Total In all More than In addition and Minus Decrease Difference Subtract Less than Decrease by Fewer than Per Times Product Multiplied Each Factors Rate Ratio Divided Quotient Separate Is Same as Similar Equal to

Writing Algebraic Expressions O There is an important concept to remember when writing algebraic expressions or equations. Write a model of the situation using words. Define the variable Write an algebraic expression or equation

O Write five years older than her brother as an algebraic expression. O Words – five years older than her brother as an algebraic expression O Variable – O Let a represent her brother’s age. O Expression – Five yearsolder thanher brother’s age 5 +a O The expression is 5 + a Writing Algebraic Expressions

O Write the following as an algebraic expression seconds faster than Tina’s time. 2. The difference between 7 and a number. 3. The quotient of a number and nine. Answers: 1. t n or n n/9 Writing Algebraic Expressions

O Write a number less than 8 is 22 O Words – a number less than 8 is 22 O Variable – O Let n represent the number. O Equation – A numberless than 8is22 n -8= 22 O The equation is n – 8 = 22 Writing Algebraic Equations

O Write two times a number plus 10 is 65 O Words – two times a number plus 10 is 65 O Variable – O Let n represent the number. O Equation – Two times a numberplus 10 is 65 2 (x)n + 10 = 65 O The equation is 2n + 10 = 65 Writing Two Step Equations

Writing Equations w/variables on Both Sides O Write eight plus four times a number is five times the number. O Words – eight plus four times a number is five times a number. O Variable – O Let n represent the number. O Equation – eight plus four times a number is five times a number (x) n = 5 (x) n O The equation is 8 + 4n = 5n

Writing Multi-Step Equations O Translate; three times the sum of a number and 4 is 32. O Words – three times the sum of a number and 4 is 32 O Variable – O Let n represent the number. O Equation – Three times (the sum of a number and 4) is 32 3 (x) ( n + 4 ) = 32 O The equation is 3 ( n + 4) = 32

Using Equations to Solve Real World Problems O A New York taxi cab driver charges his passengers $2.25 for each fare plus an additional $1.50 per mile traveled. The total ride for one passenger was $ How many miles did the passenger ride in the taxi cab? O Write the Equation and solve : m = m = m = 7 miles

Summarize/Reflect O What do you now know about writing expressions and equations? O Is there anything else you would want to learn about writing expressions or equations? O Can you answer the essential question to this lesson?